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  1. Journal of Mathematical Fluid Mechanics
  2. Journal of Mathematical Fluid Mechanics : Volume 16
  3. Journal of Mathematical Fluid Mechanics : Volume 16, Issue 4, December 2014
  4. The Rot-Div System in Exterior Domains
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Journal of Mathematical Fluid Mechanics : Volume 19
Journal of Mathematical Fluid Mechanics : Volume 18
Journal of Mathematical Fluid Mechanics : Volume 17
Journal of Mathematical Fluid Mechanics : Volume 16
Journal of Mathematical Fluid Mechanics : Volume 16, Issue 4, December 2014
Local Controllability to Trajectories of the Magnetohydrodynamic Equations
Instability of Equatorial Water Waves with an Underlying Current
Strong L p -Solutions of the T α-Type Navier–Stokes Equation and the Regularizing-Decay Rate Estimation
Hölder Continuity of Solutions to the Kinematic Dynamo Equations
The Rot-Div System in Exterior Domains
A Weak-L p Prodi–Serrin Type Regularity Criterion for the Navier–Stokes Equations
Nonlinear Stability of Convection in a Porous Layer with Solid Partitions
Liquid Bridges Between Contacting Balls
On the Regularity of Weak Solutions to the MHD System Near the Boundary
Incompressible Limit for the Compressible Flow of Liquid Crystals
On a Nonlinear Model for Tumor Growth: Global in Time Weak Solutions
Noise Prevents Infinite Stretching of the Passive Field in a Stochastic Vector Advection Equation
Higher Integrability of Solutions to Generalized Stokes System Under Perfect Slip Boundary Conditions
Journal of Mathematical Fluid Mechanics : Volume 16, Issue 3, September 2014
Journal of Mathematical Fluid Mechanics : Volume 16, Issue 2, June 2014
Journal of Mathematical Fluid Mechanics : Volume 16, Issue 1, March 2014
Journal of Mathematical Fluid Mechanics : Volume 15
Journal of Mathematical Fluid Mechanics : Volume 14
Journal of Mathematical Fluid Mechanics : Volume 13
Journal of Mathematical Fluid Mechanics : Volume 12
Journal of Mathematical Fluid Mechanics : Volume 11
Journal of Mathematical Fluid Mechanics : Volume 10
Journal of Mathematical Fluid Mechanics : Volume 9
Journal of Mathematical Fluid Mechanics : Volume 8
Journal of Mathematical Fluid Mechanics : Volume 7
Journal of Mathematical Fluid Mechanics : Volume 6
Journal of Mathematical Fluid Mechanics : Volume 5
Journal of Mathematical Fluid Mechanics : Volume 4
Journal of Mathematical Fluid Mechanics : Volume 3
Journal of Mathematical Fluid Mechanics : Volume 2
Journal of Mathematical Fluid Mechanics : Volume 1

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The Rot-Div System in Exterior Domains

Content Provider SpringerLink
Author Pokorný, Milan Mucha, Piotr B.
Copyright Year 2014
Abstract The goal of this paper is to reconsider the classical elliptic system rot v =  f, div v =  g in simply connected domains with bounded connected boundaries (bounded and exterior sets). The main result shows solvability of the problem in the maximal regularity regime in the L p -framework taking into account the optimal/minimal requirements on the smoothness of the boundary. A generalization for the Besov spaces is studied, too, for $${{\bf f} \in \dot B^s_{p,q}(\Omega)}$$ for $${-1+\frac 1p < s < \frac 1p}$$ . As a limit case we prove the result for $${{\bf f} \in \dot B^0_{3,1}(\Omega)}$$ , provided the boundary is merely in $${B^{2-1/3}_{3,1}}$$ . The dimension three is distinguished due to the physical interpretation of the system. In other words we revised and extended the classical results of Friedrichs (Commun Pure Appl Math 8;551–590, 1955) and Solonnikov (Zap Nauch Sem LOMI 21:112–158, 1971).
Ending Page 720
Page Count 20
Starting Page 701
File Format PDF
ISSN 14226928
e-ISSN 14226952
Journal Journal of Mathematical Fluid Mechanics
Issue Number 4
Volume Number 16
Language English
Publisher Springer Basel
Publisher Date 2014-08-07
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Mathematical Methods in Physics optimal regularity Boundary value problems for first-order elliptic systems Fluid- and Aerodynamics exterior domain A priori estimates Linear first-order systems Rot-div system a-priori estimates Besov spaces Classical Continuum Physics
Content Type Text
Resource Type Article
Subject Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics
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